Answer each of the questions on your own paper. Put your name on each page of your paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. A table of laplace transforms and the statement of the main partial fraction decomposition theorem have been appended to the exam. There are 60 points possible: [10 points] compute the laplace transform of each of the following functions. 2y + 5y + 2y = cos 2t, y(0) = 3, y (0) = 2. Note that you are asked to nd y (s), but not y(t): [12 points] compute the inverse laplace transform of each of the following rational functions. (a) f (s) = 3s2 + 3s 1 (s + 1)(s + 2)(s 3) (b) g(s) = You may use whatever method you prefer. y + 6y + 8y = 5e 4t.
